1. A seismograph consists of a mass m : 2kg attached via a spring with constant k : 50N/m to a support that moves horizontally with Earth's surface. Its purpose is to measure Earth's motion $E(t) by tracing the displacement of the support relative to the mass (for example, using a pen and rotating drum). In principle, if the mass m were innitely heavy, it would not move (relative to an inertial frame), and the pen would record just Earth's displacement, in practice, it moves.| inc/(HM mam\" x; l.-'9 .q :5 \"Min; m - 2.0 ka l 6/ dim), " ' g "'5'?" : Wn k : 50 \"(M l / / / / / / /// $21,) 5'34\"!" GINA\". The mass is immersed in a fluid of negligible mass, which provides a viscous force Fzm': with r=8%. The spring and viscous forces depend only on the relative displacement 33(t) and velocity. (a) Show that the relative displacement 93(t) satises the equation: mi+r5c+kcc= m:'i:E. Even if you do not show this, you can still use it for the next part. (b) During a small earthquake, Earth's vibration is described by the formula: 5t mE(t) = 1.5cos (s) mm. Find a formula for the steady state oscillations of :c(t). If the traced signal is written as :c(t) = Acos(5 gt), what are its amplitude A and phase gt